Dynamical properties of a resonator can be analyzed using the Rayleigh-Lorentz invariant which is not an exact constant but varies more or less over time. We investigate the time behavior of this invariant for a flux qubit resonator in order for better understanding of qubit-information detection with the resonator. Flux qubit resonators can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of qubit resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.
We discuss the ground state entanglement of a bi-partite system, composed by a qubit strongly interacting with an oscillator mode, as a function of the coupling strenght, the transition frequency and the level asymmetry of the qubit. This is done in the adiabatic regime in which the time evolution of the qubit is much faster than the oscillator one. Within the adiabatic approximation, we obtain a complete characterization of the ground state properties of the system and of its entanglement content.
The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage (STIRAP) should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechnical resonator by vacuum-stimulated adiabatic passage wit…
Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their application in quantum information processing. In this paper, we propose a quantum speedup method for adiabatic creation of cat states in a Kerr nonlinear resonator via gradient-descent optimal adiabatic control. By simultaneously adiabatic tuning the the cavity detuning and driving field strength, the width of minimum energy gap between the target trajectory and non-adiabatic trajectory can be widen, which allows us to speed up the evolution along the adiabatic path. Compar…
We demonstrate Purcell-like enhancement of Rayleigh scattering into a single optical mode of a Fabry-Perot resonator for several thermal atomic and molecular gases. The light is detuned by more than an octave, in this case by hundreds of nanometers, from any optical transition, making particle excitation and spontaneous emission negligible. The enhancement of light scattering into the resonator is explained quantitatively as an interference effect of light waves emitted by a classical driven dipole oscillator. Applications of our method include the sensitive, non-destructive in-situ detection …
An adiabatic method for a single-shot non-demolition measurement of the phase qubit is suggested. The qubit is inductively coupled to a low-frequency resonator, which in turn is connected with a classical measurement device (phase meter). The resonator drives adiabatic oscillations of the supercurrent in the qubit loop. The back reaction of the qubit loop on the resonator depends on the qubit state. Measuring the phase shift of the resonator's oscillations one can determine the state of the qubit. Numerical computations with available experimental parameters show that the phase difference betw…
The main challenge in deterministic quantum state transfer in long-distance quantum communications is the transmission losses in the communication channel. To overcome this limitation, here we use the adiabatic theorem and find a lossless evolution path between two remote mechanical modes. By adiabatic variation of the effective coupling strengths between the two nodes and the intermediate optical channel modes, we engineer a transmission path for the quantum state transfer that is decoupled from the decaying fiber modes. Using our proposed method we show that one obtains a quantum state trans…
Adiabatic wavelength conversion is experimentally demonstrated at a single photon power-level using an integrated Silicon ring resonator. This approach allows conversion of a photon to arbitrary wavelengths with no energy or phase matching constraints. The conversion is inherently low-noise and efficient with greater than 10% conversion efficiencies for wavelength changes up to 0.5nm, more than twenty times the resonators line-width. The observed wavelength change and efficiency agrees well with theory and bright coherent light demonstrations. These results will enable integrated quantum optic…
We present experiments where a single subwavelength scatterer is used to examine and control the back-scattering induced coupling between counterpropagating high-Q modes of a microsphere resonator. Our measurements reveal the standing wave character of the resulting symmetric and antisymmetric eigenmodes, their unbalanced intensity distributions, and the coherent nature of their coupling. We discuss our findings and the underlying classical physics in the framework common to quantum optics and provide a particularly intuitive explanation of the central processes.
We propose a way for implementing quantum information transfer with two superconducting flux qubits, by coupling them to a resonator. This proposal does not require adjustment of the level spacings or uniformity in the device parameters. Moreover, neither adiabatic passage nor a second-order detuning is needed by this proposal, thus the operation can be performed much faster when compared with the previous proposals.
The main challenge in deterministic quantum state transfer between remote mechanical resonators is the local decoherence and the transmission losses in the communication channel. In the path of overcoming this limitation, here we employ a shortcut to adiabatic passage protocol to devise a fast and reliable evolution path between two remote mechanical modes in separate optomechanical systems. A quantum state transfer between the two nodes is conceived by engineering their coupling to an intermediate fiber optical channel. The coupling pulses are operated such that the dark eigenmode of the syst…
We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or rais…
We use the Rayleigh-Schrödinger perturbation theory to calculate the corrections to the adiabatic geometric phase due to a perturbation of the Hamiltonian. We show that these corrections are at least of second order in the perturbation parameter. As an application of our general results we address the problem of the adiabatic geometric phase for a one-dimensional particle which is confined to an infinite square well with moving walls.
Spectral properties of a quantum circuit are efficiently read out by monitoring the resonance frequency shift it induces in a microwave resonator coupled to it. When the two systems are strongly detuned, theory attributes the shift to an effective resonator capacitance or inductance that depends on the quantum circuit state. At small detuning, the shift arises from the exchange of virtual photons, as described by the Jaynes-Cummings model. Here we present a theory bridging these two limits and illustrate, with several examples, its necessity for a general description of quantum circuits readou…
We study a Rabi type Hamiltonian system in which a qubit and a d-level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is a found of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppress the bipartite e…
We consider an all in-fiber optical modulator based on a ring resonator configuration. The case of adiabatic to nonadiabatic transition is considered, where the geometrical (Berry) phase acquired in a round trip along the ring changes abruptly by pi. Degradation of the responsivity of the modulator due to finite linewidth of the optical input is discussed. We show that the responsivity of the proposed modulator can be significantly enhanced with optimum design and compare with other configurations.
We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can readily access both the adiabatic and anti-adiabatic regimes of this model. Strong e-ph coupling required for small-polaron formation can also be reached. We show that small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-c…
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyse the system by the adiabatical approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Energy-level spectrum of the system in the adiabatical displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution.
We study theoretically a radio frequency superconducting interference device integrated with both a nanomechanical resonator and an LC one. By applying adiabatic and rotating wave approximations, we obtain an effective Hamiltonian that governs the dynamics of the mechanical and LC resonators. Nonlinear terms in this Hamiltonian can be exploited for performing a quantum nondemolition measurement of Fock states of the nanomechanical resonator. We address the feasibility of experimental implementation and show that the nonlinear coupling can be made sufficiently strong to allow the detection of d…
We propose an efficient scheme for the implementation of quantum information transfer in a onedimensional coupled resonator waveguide. We show that, based on the effective long-range dipole-dipole interactions between the atoms mediated by the cavity modes, Raman transitions between the atoms trapped in different nodes can take place. Quantum information could be transferred directly between the opposite ends of the coupled waveguide without involving the intermediate nodes via either Raman transitions or the stimulated Raman adiabatic passages. Since this scheme, in principle, is a one-step p…
Cavity cooling via quantum backaction force can extract thermal fluctuations from a mechanical resonator to reach the quantum ground state. Surface or bulk two-level-system (TLS) defects in a mechanical resonator can couple with the mechanical mode via deformation potential and affect the cooling process significantly. Here, we develop a theory to study the cavity cooling of a mechanical mode in the presence of a TLS defect using the adiabatic elimination technique. Our result shows that the cooling process depends strongly on the resonance and the damping rate of the TLS.
We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.
The process of measurement of a phase qubit by a resonant microwave cavity is considered for various interactions between the qubit and the cavity. A novel quasiclassical approach is described based on adiabatic reversals of the qubit state by an effective field. A similar approach was implemented earlier for the detection of electron and nuclear spins using magnetic resonance force microscopy (MRFM), but this approach has not previously been used for the measurement of a quantum state. Quasiclassical and quantum regimes are described. We consider both linear and nonlinear resonators. The effe…
Quantum manipulation of mechanical resonators has been widely applied in fundamental physics and quantum information processing. Among them, cooling the mechanical system to its quantum ground state is regarded as a key step. In this work, we propose a scheme which one can realize ground-state cooling of resonator in a cavity magnomechanical system. The system consists of a microwave cavity and a small ferromagnetic sphere, in which phonon-magnon coupling and cavity photon-magnon coupling can be achieved via magnetostrictive interaction and magnetic dipole interaction, respectively. After adia…
Quantum manipulation of coupled mechanical resonators has become an important research topic in optomechanics because these systems can be used to study the quantum coherence effects involving multiple mechanical modes. A prerequisite for observing macroscopic mechanical coherence is to cool the mechanical resonators to their ground state. Here we propose a theoretical scheme to cool two coupled mechanical resonators by introducing an optomechanical interface. The final mean phonon numbers in the two mechanical resonators are calculated exactly and the results show that the ground-state coolin…
We propose and study an approach to realize quantum switch for single-photon transport in a coupled superconducting transmission line resonator (TLR) array with one controllable hopping interaction. We find that the single-photon with arbitrary wavevector can transport in a controllable way in this system. We also study how to realize controllable hopping interaction between two TLRs via a superconducting quantum interference device (SQUID). When the frequency of the SQUID is largely detuned from those of the two TLRs, the variables of the SQUID can be adiabatically eliminated and thus a contr…
A hybrid quantum system consisting of spatially separated two-level atoms is studied. Two atoms do not interact directly, but they are coupled via an intermediate system which is consisting of a superconducting flux qubit interacting with a mechanical and an electrical resonator which are coupled to one of the atoms. Moreover, the superconducting flux qubit is driven by a classical microwave field. Applying the adiabatic elimination an effective Hamiltonian for the atomic subsystem is obtained. Our results demonstrate that the entanglement degradation decay as well as the fidelity decay in the…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting qubit as a non-linear probe of the phase, otherwise unobservable due to the linearity of the oscillator. Our results demonstrate that the geometric phase is, for a variety of cyclic trajectories, proportional to the area enclosed in the quadrature plane. At the transition to the non-adiabatic regime, we study corrections to the phase and dephasing of the qubi…
In this paper, we propose a scheme to realize three-qubit quantum phase gate of one qubit simultaneously controlling two target qubits using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The two lowest levels |0> and |1> of each SQUID are used to represent logical states while the higher energy levels |2> and |3> are utilized for gate realization. Our scheme does not require adiabatic passage, second order detuning, and the adjustment of the level spacing during gate operation which reduce the gate time significantly. The scheme is gen…
Hybrid quantum systems have been developed with various mechanical, optical and microwave harmonic oscillators. The coupling produces a rich library of interactions including two mode squeezing, swapping interactions, back-action evasion and thermal control. In a multimode mechanical system, coupling resonators of different scales (both in frequency and mass) leverages the advantages of each resonance. For example: a high frequency, easily manipulated resonator could be entangled with a low frequency massive object for tests of gravitational decoherence. Here we demonstrate coherent optomechan…
We analyze a single-shot readout for superconducting qubits via the controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonator from the transmission line during the dispersive qubit-resonator interaction, thus circumventing damping from the Purcell effect. We show that if the qubit frequency tuning is sufficiently adiabatic, a fast high-fidelity qubit readout is possible, even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes-Cummings nonlinearity leads to the quadrature squeezing of the resonator field bel…
We propose to realize mechanical parity-time PT symmetry in two coupled optomechanical systems. To provide gain to one mechanical resonator and the same amount of damping to the other, the two optical cavities should be driven by blue- and red-detuned laser fields, respectively. After adiabatically eliminating the degrees of freedom of the cavity modes, we derive a formula to describe the PT symmetry of two coupled mechanical resonators. Mechanical PT-symmetric phase transition is demonstrated by the dynamical behavior of the mechanical resonators. Moreover, we study the effect of the quantum …
We propose a scheme for generating a genuine $χ$-type four-particle entangled state of superconducting artificial atoms with broken symmetry by using one-dimensional transmission line resonator as a data bus. The $Δ$-type three-level artificial atom we use in the scheme is different from natural atom and has cyclic transitions. After suitable interaction time and simple operations, the desired entangled state can be obtained. Since artificial atomic excited states and photonic states are adiabatically eliminated, our scheme is robust against the spontaneous emissions of artificial atoms and th…
We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction allows to employ tools from center manifold theory and geometric singular perturbation theory to eliminate the variables associated to the environment (adiabatic elimination) with high-order accuracy. An important specificity is to preserve the quantum structure: reduced dynamics in (positive) Lindblad form and coordinate mappings in Kraus form. We provide formul…
A dilutely filled $N$-site optical lattice near zero temperature within a high-$Q$ multimode cavity can be mapped to a spin ensemble with tailorable interactions at all length scales. The effective full site to site interaction matrix can be dynamically controlled by the application of up to $N(N+1)/2$ laser beams of suitable geometry, frequency and power, which allows for the implementation of quantum annealing dynamics relying on the all-to-all effective spin coupling controllable in real time. Via an adiabatic sweep starting from a superfluid initial state one can find the lowest energy sta…
We analyse a quantum Otto refrigerator based on a superconducting qubit coupled to two LC-resonators each including a resistor acting as a reservoir. We find various operation regimes: nearly adiabatic (low driving frequency), ideal Otto cycle (intermediate frequency), and non-adiabatic coherent regime (high frequency). In the nearly adiabatic regime, the cooling power is quadratic in frequency, and we find substantially enhanced coefficient of performance $ε$, as compared to that of an ideal Otto cycle. Quantum coherent effects lead invariably to decrease in both cooling power and $ε$ as comp…
We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states: in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function…
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where …
In this work, we demonstrate the use of frequency-tunable superconducting NbTiN coplanar waveguide microresonators for multi-frequency pulsed electron spin resonance (ESR) experiments. By applying a bias current to the center pin, the resonance frequency ($\sim$7.6 GHz) can be continuously tuned by as much as 95 MHz in 270 ns without a change in the quality factor of 3000 at 2K. We demonstrate the ESR performance of our resonators by measuring donor spin ensembles in silicon and show that adiabatic pulses can be used to overcome magnetic field inhomogeneities and microwave power limitations du…
Quantum annealing aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealer is its sensitivity to noise, and intensive research is consequently focussed towards developing noise-resilient annealers. Here we propose a new paradigm for quantum annealing with a scalable network of all-to-all connected, two-photon driven Kerr-nonlinear resonators. Each of these resonators encode an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. The fully-conne…
In modern circuit QED architectures, superconducting transmon qubits are measured via the state-dependent phase and amplitude shift of a microwave field leaking from a coupled resonator. Determining this shift requires integrating the field quadratures for a nonzero duration, which can permit unwanted concurrent evolution. Here we investigate such dynamical degradation of the measurement fidelity caused by a detuned neighboring qubit. We find that in realistic parameter regimes, where the qubit ensemble-dephasing rate is slower than the qubit-qubit detuning, the joint qubit-qubit eigenstates a…
It is known that secondary non-stoquastic drivers may offer speed-ups or catalysis in some models of adiabatic quantum computation accompanying the more typical transverse field driver. Their combined intent is to raze potential barriers to zero during adiabatic evolution from a false vacuum to a true minimum; first order phase transitions are softened into second order transitions. We move beyond mean-field analysis to a fully quantum model of a spin ensemble undergoing adiabatic evolution in which the spins are mapped to a variable mass particle in a continuous one-dimensional potential. We …
With the assistance of a single cyclic three-level system, which can be realized by a superconducting flux qubit, we study theoretically the degenerate microwave parametric down-conversion (PDC) in a superconducting transmission line resonator with the fundamental and second harmonic modes involved. By adiabatically eliminating the excited states of the three-level system, we obtain an effective microwave PDC Hamiltonian for the two resonator modes in such a circuit QED system. The corresponding PDC efficiency in our model can be much larger than that in the similar circuit QED system based on…
We study arrays of mechanical oscillators in the quantum domain and demonstrate how the motions of distant oscillators can be entangled without the need for control of individual oscillators and without a direct interaction between them. These oscillators are thought of as being members of an array of nano-electromechanical resonators with a voltage being applicable between neighboring resonators. Sudden non-adiabatic switching of the interaction results in a squeezing of the states of the mechanical oscillators, leading to an entanglement transport in chains of mechanical oscillators. We disc…
We investigate a non-adiabatic holonomic operation that enables us to entangle two fixed-frequency superconducting transmon qubits attached to a common bus resonator. Two coherent microwave tones are applied simultaneously to the two qubits and drive transitions between the first excited resonator state and the second excited state of each qubit. The cyclic evolution within this effective 3-level $Λ$-system gives rise to a holonomic operation entangling the two qubits. Two-qubit states with 95\% fidelity, limited mainly by charge-noise of the current device, are created within $213~\rm{ns}$. T…
We propose a quantum storage scheme independent of the current time-control schemes, and study a "quantum data bus" (transmission line resonator) in a hybrid system consisting of a circuit QED system integrated with a cold molecular ensemble. Here, an effective interaction between charge qubit and molecule is mediated by the off-resonate field in the data bus. Correspondingly, the charge state can be mapped into the collective quasi-spin state of the molecular ensemble via the standard dark state based adiabatic manipulation.
We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely …
We examine the development of the concept of parametric invariance in classical mechanics, quantum mechanics, statistical mechanics, and thermodynamics, and particularly its relation to entropy. The parametric invariance was used by Ehrenfest as a principle related to the quantization rules of the old quantum mechanics. It was also considered by Rayleigh in the determination of pressure caused by vibration, and the general approach we follow here is based on his. Specific calculation of invariants in classical and quantum mechanics are determined. The Hertz invariant, which is a volume in phas…
